Rose went down 5-2 at home to Rangers B in their last league outing – ending a run of eight wins in a row.
Robbie Horn’s side still top the table but the Ibrox youngsters are now just a point behind with two games in hand.
East Kilbride, champions twice in the last five seasons, are currently in unfamiliar territory down in ninth spot. But Horn fully expects a tough test against a side packed with experience.
He said: “East Kilbride have picked up recently and have had decent results.
"They have got really good, experienced players in their team - Steven Old, Chris Millar, Lee Miller, Chris Erskine - who have all been real top players going back.
"Connor Brennan is a good goalkeeper and they've managed to bring in a couple of loan players as well so it's going to be a really tough game.
"They didn't start the season great but I think they had a lot of injuries and issues but they've managed to get a settled team back on the park again and you can see that with the results they're starting to get.
"It will be a really tough game and we've just got to get back to the levels we were showing before the Rangers game, when we let ourselves down a wee bit."
Rose bounced back from their Rangers defeat on Saturday when a 2-0 win at Forres Mechanics saw them safely through to the second round of the Scottish Cup and another, though somewhat shorter, away tie at fellow Lowland League side East Stirlingshire.
Keiran McGachie gave Rose the lead in the 33rd minute at Forres, although they had to wait until the 90th minute before making absolutely sure of their place in the next round as George Hunter curled home a second.
"In the first half we probably should have been further in front, we didn't take the opportunities that we did have and it just made it a wee bit more uncomfortable than it probably should have been,” admitted Horn.
"I don't think they created a lot - we defended pretty well and dealt with most things coming in. We just didn't have that clinical edge to finish them off before we did.
"But the most important thing is we're through to the next round."
On the draw with Shire he said: "It could have been a harder tie, it could have been an easier one.
"It's a team we know from playing in the same league as us and it will be a very difficult game away from home so we'll have to be at our best to get a result.